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What Can We Say After We Say We're Sorry? or, Adventures in Optimization

Margaret Wright brought real world problems and the practice of optimization together for her talk, titled "What Can We Say After We Say We're Sorry? or, Adventures in Optimization," on Wednesday, March 5 at the MAA’s Carriage House.

Wright, who carries the title of Silver Professor of Computer Science and Mathematics, and chair of the Computer Science Department in the Courant Institute of Mathematical Sciences at New York University, brought a few of her personal experiences in real world optimization to show the audience that a lot of practical problems take can the form of optimization problems. Audio

Wright made the point that you can succeed if you can take somebody’s problem and improve upon its solution, even if that solution is not perfect. “In mathematics, optimization means finding…or computing a highly accurate optimal solution, possibly a global solution…” Wright said. “But in practice…you can’t always do this.”

Wright’s first example was a project she worked on at the Stanford Linear Accelerator Center (SLAC) in 1986. SLAC is home to an expensive, two-mile long accelerator that runs underground and is used for research in several scientific fields.

“Back then, electricity was so expensive they could only keep the accelerator on half of the year,” Wright said. “So they would turn it off for a period of time, but when they’d turn it back on, the beam of electrons would no longer be straight.” Wright and her team were brought in to find a more efficient solution for commissioning, or recalibrating, the beam then the previously used practice of adjusting the accelerator’s hundreds of magnets one at a time (a practice known as “knobbing”). Using a special form of a sequential quadratic programming algorithm, Wright’s team was able to reduce commissioning time from a couple of weeks, to a single eight hour shift.

Wright then spoke about a project she worked on while employed at Bell Laboratories. One of their biggest customers, The Home Depot, wanted an indoor wireless communication system with the maximum amount of coverage possible throughout the store. This required a number of complex radio propagation models and precise measurements that were made extra difficult by the complicated layout of a Home Depot store. Wright’s team knew they had to maximize a function with several variables, and it would be tough to get a high accuracy solution, but in the end they were able to find an optimal solution that, while not perfect, was good enough for the customer. Audio

To conclude her talk, Wright drove home the point that the solutions her teams came up with in her two examples were not exact solutions (like the solution to a math homework problem), but rather they “helped people get better solutions to real world problems.”

“I don’t know if I can convey it without leaping up and down,” Wright exclaimed, “but there is such joy for mathematicians in helping to solve real world problems.” —Ryan Miller